Question

A boy threw a baseball upward from a dormitory window. The height of the ball above the ground, in feet , is determined by height = -16x^2 + 68x + 29 Where x is the number of seconds after the baseball is thrown from the window A)determine the height of the ball 2 seconds after it is thrown out the window. Feet =B) Determine the height of the ball 4 seconds after it is thrown out the window Feet =

Answer 1

What we have here is a function which is used to determine the height (which is h) x seconds of a ball, after it is thrown.

The function used is;

$f(x)=-16x^2+68x+29$

To determine the height of the ball after 2 seconds, we shall input the value 2 into the function, instead of x. We now have the following;

$\begin{gathered} f(x)=-16x^2+68x+29 \\ f(2)=-16(2)^2+68(2)+29 \\ f(2)=-16(4)+136+29 \\ f(2)=-64+165 \\ f(2)=101 \end{gathered}$

This means, after 2 seconds of being thrown, the ball is 101 feet in the air.

To determine the height 4 seconds after the ball is thrown out the window, we shall use the same procedure and this time, the input will be 4 and not 2. Hence;

$\begin{gathered} f(x)=-16x^2+68x+29 \\ f(4)=-16(4)^2+68(4)+29 \\ f(4)=-16^{}(16)+272+29 \\ f(4)=-256+301 \\ f(4)=45 \end{gathered}$

The result shows that after 4 seconds of being thrown, the ball is 45 feet in the air.

ANSWER:

(A) 101 feet

(B) 45 feet